Last page of booklet prints too dark

Are you viewing your pdf in Acrobat or Reader? It looks ok here on a Mac.

I opened page 10 in Illustrator and was able to copy the vector art from Illustrator and paste it into InDesign without any issues, when I tried this with page 12, the vector art was a font (missing in Illustrator). Perhaps you converted the other art to outlines (page 10) but accidently neglected to convert the art on page 12, or the type is grouped with the vector art? it's hard to say. If you are pasting the art into InDesign, set your clipboard preference to "Prefer pdf when pasting".

Edit, you might see improvement executing to PDF/X-4, but all the letter art should be consistent vector art.

If possible, put 1 or 2 blank pages at the end of the booklet and reprint, so that this page is (effectively) the last page but physically moved forward a bit. This could be an anomaly of how the printer is handling the pages, rather than an ID/document issue.

You might also export the booklet to PDF and see if the page image shows the same darkening, which would indicate it's both a document issue and something oddball about that page.

Hard to say without seeing the file. Does the image include the background or are you layering the black onto a separate background?

Is there a blend mode or transparency assgned to the image on one page and not the other? (like Multiply)

Also: the top image looks lower resolution than the bottom one.